Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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POSET METRICS ADMITTING ASSOCIATION SCHEMES AND A NEW PROOF OF MACWILLIAMS IDENTITY

  • Oh, Dong Yeol (Division of Liberal Arts Hanbat National University)
  • Received : 2012.02.02
  • Published : 2013.09.01
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Abstract

It is known that being hierarchical is a necessary and sufficient condition for a poset to admit MacWilliams identity. In this paper, we completely characterize the structures of posets which have an association scheme structure whose relations are indexed by the poset distance between the points in the space. We also derive an explicit formula for the eigenmatrices of association schemes induced by such posets. By using the result of Delsarte which generalizes the MacWilliams identity for linear codes, we give a new proof of the MacWilliams identity for hierarchical linear poset codes.

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References

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  1. Characterization of Metrics Induced by Hierarchical Posets vol.63, pp.6, 2017, https://doi.org/10.1109/TIT.2017.2691763